Negri

Negri

Subgroups	2.3.5, 2.3.5.7, 2.3.5.7.13
Reduced mapping	⟨1; -4 3 -2 -3]
ET join	10 & 19
Generators (CWE)	~16/15 = 125.4¢
MOS scales	1L 8s, 9L 1s, 10L 9s
Ploidacot	omega-tetracot
Comma basis	16875/16384 (2.3.5); 49/48, 225/224 (2.3.5.7); 49/48, 65/64, 91/90 (2.3.5.7.13)
Minimax error	7-odd-limit: 17.8¢; 2.3.5.7.13 15-odd-limit: 17.8¢
Target scale size	7-odd-limit: 8 notes; 2.3.5.7.13 15-odd-limit: 19 notes

Negri, 19 & 29, is a low-accuracy 5-limit temperament that splits 4/3 into four sharp 16/15's, each approximately the size of 14/13. It enables the following comma loop progression (written here in 19edo notation):

F C F A
A C E (F -> A: 5/4 up)
E B E G# (A -> E: 4/3 down)
G# B D# (E -> G#: 5/4 up)
D# A# D# Fx (G# -> D#: 4/3 down)
Fx A# Cx = Gb Bbb Db (D# -> Fx: 5/4 up)
Db Ab Db F (Gb -> Db: 4/3 down)
F C F A (Db -> F: 5/4 up)

Extensions

Negri has an endoparticular extension to 2.3.5.7.13 via tempering out 49/48 and 676/675, called negrisept. It also has a 7-limit weak extension Semibuzzard, splitting the octave into two 7/5's, which tempers out 50/49 and the Buzzard comma 65536/64827 instead.

List of patent vals

The following patent vals support 5-limit Negri, not including vals contorted in the 5-limit.

Edo	Generator	Fifth
1	0	1200.000
10	120	720.000
29	124.138	703.448
48	125	700.000
19	126.316	694.737
47	127.660	689.362
28	128.571	685.714
9	133.333	666.667